## Hokkaido Mathematical Journal

### Regular homeomorphisms of $\mathbb{R}^3$ and of $\mathbb{S}^3$

#### Abstract

This paper is the paper announced in [Be2, References [2]]. We show that every compact abelian group of homeomorphisms of $\mathbb{R}^3$ is either zero-dimensional or equivalent to a subgroup of the orthogonal group O(3). We prove a similar result if we replace $\mathbb{R}^3$ by $\mathbb{S}^3$, and we study regular homeomorphisms that are conjugate to their inverses.

#### Article information

Source
Hokkaido Math. J., Volume 47, Number 2 (2018), 351-371.

Dates
First available in Project Euclid: 18 June 2018

https://projecteuclid.org/euclid.hokmj/1529308823

Digital Object Identifier
doi:10.14492/hokmj/1529308823

Mathematical Reviews number (MathSciNet)
MR3815297

Zentralblatt MATH identifier
06901710

#### Citation

REJEB, Khadija Ben. Regular homeomorphisms of $\mathbb{R}^3$ and of $\mathbb{S}^3$. Hokkaido Math. J. 47 (2018), no. 2, 351--371. doi:10.14492/hokmj/1529308823. https://projecteuclid.org/euclid.hokmj/1529308823